Question

Two circularly shaped linear polarisers are placed coaxially. The transmission axis of the first polariser is at $30^{\circ}$ from the vertical while the second one is at $60^{\circ}$, both in the clockwise sense. If an unpolarised beam of light of intensity $I=20 \,W / m ^{2}$ is incident on this pair of polarisers, then the intensities $I_{1}$ and $I_{2}$ transmitted by the first and second polarisers

• A. $I_1 = 10.0 W/m^2$ and $I_2 = 7.5 W/m^2$
• B. $I_1 = 20 W/m^2$ and $I_2$ = $15 W/m^2$
• C. $I_1 = 10.0 W/m^2$ and $I_2 = 8.6 W/m^2$
• D. $I_1 = 15.0 W/m^2$ and $I_2$ = 0.0 $W/m^2$

Answer 1

Answer: (A)

$I_1 = 10.0 W/m^2$ and $I_2 = 7.5 W/m^2$

Answer 2

As beam incident over first polaroid is unpolarised, its intensity is reduced to half (Malus' law is not applicable).
So, intensity $I_{1}$ after first polaroid is
$I_{1}=\frac{I_{0}}{2}=\frac{20}{2}=10 \,Wm ^{-2}$
As light from first polaroid is polarised, Malus' law is now applicable.
So, intensity $I_{2}$ obtained after second polaroid is
$I_{2}=I_{1} \cdot \cos ^{2} \theta$
where, $\theta=$ angle between transmission axis of first and second polaroid.
So, $I_{2}=10 \times \cos ^{2} 30^{\circ}$
$=10 \times\left(\frac{\sqrt{3}}{2}\right)^{2}=7.5\, Wm ^{-2}$